Network topologies define the layout of connections between nodes in a computer network. The physical topology refers to the actual layout of cables and connections, while the logical topology defines how data is transmitted. Common network topologies include bus, star, ring, mesh, and tree. Each has advantages and disadvantages depending on the network size and needs. The bus topology is inexpensive but has limitations on cable length and number of devices. Star topology is robust but requires more cable and hardware. Ring topology has no central point of failure but a single fault disables the whole network. Mesh networks are highly redundant but also complex and expensive to implement.